Graphene-based membrane and method of preparation thereof

ABSTRACT

A method of preparing a graphene-based membrane is provided. The method may include providing a stacked arrangement of layers of a graphene-based material, wherein the layers of the graphene-based material define one or more nanochannels between neighboring layers, and varying an electrical charge on a surface of the layers of the graphene-based material defining the one or more nanochannels to control size selectivity and/or ionic selectivity of the graphene-based membrane. A graphene-based membrane and a method of separating ions from a fluid stream are also provided.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of priority of U.S. ProvisionalPatent Application No. 62/386,274 filed on Nov. 24, 2015, the content ofwhich is incorporated herein by reference in its entirety for allpurposes.

TECHNICAL FIELD

Various embodiments relate to a graphene-based membrane, method ofpreparing the graphene-based membrane, and method of separating ionsfrom a fluid stream.

BACKGROUND

Water flux, ionic selectivity, ionic rejection rate, and molecular/ionicsize cutoff are some of the parameters that determine performance ofwater filtration membranes. Improving any of these parameters may resultin a better and more energy efficient filtration or desalinationmembrane.

Graphene-based membranes exhibiting ultra-high water flux have recentlyattracted significant attention as molecular and ionic sieves.Particularly, nanostructured graphene-oxide (GO) laminatemembranes—scalable, inexpensive, thermally and chemically robust, andintegratable with current technologies—are enticing candidates for thenext generation of filtration or desalination membrane. Ionic rejectionof the graphene-based membranes may be driven by geometric sizeexclusion, and size of nanochannels in GO membranes may be decreased toachieve a much smaller cutoff size required for application such asdesalination. The improvement in ionic rejection carried out by sizereduction of nanochannels in GO membranes, however, negatively impactswater flux, which affects performance of the membranes and theiradoption in industry.

In view of the above, there exists a need for a membrane that exhibitsimproved ionic rejection and/or ion selectivity levels while achievingor maintaining acceptable water flux performance that addresses or atleast alleviates one or more of the above-mentioned problems.

SUMMARY

In a first aspect, a method of preparing a graphene-based membrane isprovided. The method comprises

-   -   a) providing a stacked arrangement of layers of a graphene-based        material, wherein the layers of the graphene-based material        define one or more nanochannels between neighboring layers, and    -   b) varying an electrical charge on a surface of the layers of        the graphene-based material defining the one or more        nanochannels to control size selectivity and/or ionic        selectivity of the graphene-based membrane.

In a second aspect, a graphene-based membrane is provided. Thegraphene-based membrane comprising a stacked arrangement of layers of agraphene-based material, the layers of the graphene-based materialdefining one or more nanochannels between neighboring layers, wherein asurface of the layers of the graphene-based material defining the one ormore nanochannels possess an electrical charge, and wherein the layersof the graphene-based material are configured to control sizeselectivity and/or ionic selectivity of the graphene-based membrane byvarying the electrical charge.

In a third aspect, a method of separating ions from a fluid stream isprovided. The method comprises

-   -   a) providing a graphene-based membrane comprising a stacked        arrangement of layers of a graphene-based material, the layers        of the graphene-based material defining one or more nanochannels        between neighboring layers, wherein a surface of the layers of        the graphene-based material defining the one or more        nanochannels possess an electrical charge, and wherein the        layers of the graphene-based material are configured to control        size selectivity and/or ionic selectivity of the graphene-based        membrane by varying the electrical charge, and    -   b) directing a fluid stream comprising one or more ions towards        a first surface of the graphene-based membrane, wherein ions to        be separated from the fluid stream are filtered through the        graphene-based membrane.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood with reference to the detaileddescription when considered in conjunction with the non-limitingexamples and the accompanying drawings, in which:

FIG. 1 is a schematic diagram showing preparation of chip-mountedgraphene oxide membranes according to an embodiment.

FIG. 2A is a graph of permeation rates of various cations and pairingcounter anion across the membranes, plotted as a function of hydrationsize of cations, demonstrating ultrahigh charge-selective permeabilityof the graphene oxide membranes.

FIG. 2B is a graph of relative cation-to-anion permeability ratiocalculated from the measured membrane potentials, demonstratingultrahigh charge-selective permeability of the graphene oxide membranes.

FIG. 2C is a graph of current-voltage curves obtained from the zerocurrent potential (or membrane potential) measurements, carried outunder asymmetric electrolyte concentrations (C_(high)/C_(low)=10) ataround pH 5.5 across the membranes, demonstrating ultrahighcharge-selective permeability of the graphene oxide membranes.

FIG. 3 is a schematic diagram showing experimental procedure for waterflux measurement across the membranes.

FIG. 4A is a graph depicting water flux versus applied pressure of a GOmembrane disclosed herein.

FIG. 4B is a graph depicting water flux versus applied pressure of a GOmembrane disclosed herein.

FIG. 4C is a graph depicting iteration testing of water fluxperformance.

FIG. 4D is a graph showing comparison of the water flux of the GO basedmembranes disclosed herein to the water flux of other types ofmembranes.

FIG. 5 is a schematic diagram providing a comparison of performances:commercial cation exchange membranes (CEM) vs graphene oxide membranes.Larger is better, except for the price. (i) represents graphene oxidemembranes according to embodiments disclosed herein, while (ii)represents the best commercial CEM membrane, dashed lines represent(iii) minimum and (iv) maximum values found in commercial membranes.

FIG. 6A is a schematic diagram showing preparation of chip-mountedgraphene oxide membranes for drift-diffusion experiment according to anembodiment. The graphene oxide membrane was mounted on a freestandingSiN_(x) membrane with a 12×12 array of square-shaped windows, separatingtwo electrolyte-filled reservoirs; Ag/AgCl electrodes in each reservoirwere used to apply an electric potential across the GO membrane and tomeasure the ionic currents flowing through the membrane.

FIG. 6B is a schematic diagram depicting ionic flow across the membrane,driven by concentration gradient (diffusion) according to an embodiment.

FIG. 6C is a schematic diagram depicting ionic flow across the membrane,driven by voltage difference (drift) according to an embodiment.

FIG. 6D is a graph showing ionic current-voltage characteristic of themembrane for different salts, measured under the concentration gradient0.1 M/0.01 M across the membrane.

FIG. 7A is a graph showing permeation rates (p) for different cations(circles) and corresponding chloride counter-ions (open and filledsquares) as a function of hydrated radius (R_(H)) of the cations areshown. The filled square represents the chloride permeability when inRbCl solution, where the hydration radii are very similar for bothions—the two-headed arrow shows the permeation difference resultingpurely from the charge rejection effects.

FIG. 7B is a schematic diagram depicting the dominant ion rejectionmechanism of size exclusion.

FIG. 7C is a schematic diagram depicting the dominant ion rejectionmechanism of electrostatic repulsion.

FIG. 7D is a graph showing permeation rates of chloride ions as afunction of the valence of the position counter-ion in the salt,revealing the effect of the correlated charge inversion in thesub-nanometer channels.

FIG. 8 is a graph showing cationic selectivity. The cationic selectivityof GO membranes for different salts, reaching values in excess of 90%.

FIG. 9A is a graph showing current-voltage (I-V) curves across themembranes at KCl salt concentration c_(KCl)=10 mM, measured fordifferent pH values.

FIG. 9B is a graph showing conductance vs pH. Dashed curve in the graphwas fitted to the mean-field model.

FIG. 9C is a graph showing permeation rates for potassium (K⁺) andchloride (Cl⁻) ions for different pH values. Dashed curves in the graphwere fitted to the mean-field model.

FIG. 9D is a graph showing ionic conductance vs molarity (circles)deviating from the Ohmic behavior (full line), even at high saltconcentrations, due to sub-nanometer channel heights. Dashed curve inthe graph was fitted to the mean-field model.

FIG. 9E is a graph showing molarity dependence for permeation rates forpotassium (K⁺) and chloride (Cl⁻) ions. Dashed curves in the graph werefitted to the mean-field model.

FIG. 9F is a graph showing molarity dependence for cation selectivity.

FIG. 10A is an atomic force microscopy (AFM) map and height profile formonolayer GO nanosheet. (Dimension Fastscan, Bruker) Two-dimensional GOnanosheets at ambient conditions were about 1 nm thick with mean planarwidth of 1 μm.

FIG. 10B is a graph showing Fourier Transform Infrared spectrum (FTIR)of air-dried GO laminates, displaying diverse functionalities such as(C—O) epoxy at 1260 cm⁻¹, (O—H) or C—O Carboxy at 1390 cm⁻¹, (C═O)Carbonyl and Carboxyl at 1718 cm⁻¹, and O—H hydroxyl at 3431 cm⁻¹.

FIG. 11A is a graph showing X-ray diffraction (XRD) spectra comparisonof dried and wet GO films. The inter-plane distance of GO reflection(100), was determined from a Rietveld refinement using conventional XRDdata and program GSAS. Using the space group P6/mmm, a Rietveldrefinement was performed with program GSAS (General Structure AnalysisSystem) until discordance factors R_(wp)=7.00%, R_(p)=5.46%,R_(Bragg)=6.33% and χ²=1.138 2. The obtained cell parameters werea=b=10.517(3) Å and c=1.9(1) Å. The investigated interlayer spacing ofdried and wet GO by XRD was around 8.5754 Å and 12.1615 Å, respectively.

FIG. 11B is a graph showing respective height profile of dried and wetGO films, measured by in-situ liquid AFM showing similar increase ininterlayer spacing after wetting.

FIG. 12A is a graph showing ionic conductances across the singlenanochannel of graphene oxide membranes, measured at three different KClconcentrations in the pH ranges of 2 to 12.

FIG. 12B is a graph showing surface charge densities as functions ofsalt concentration and pH in KCl. The charge densities were expressed interms of the amount of charged carriers per area (e/μm²).

FIG. 13A is a graph showing pH-dependent current-voltage transport ofelectrolytes exclusive of solute KCl. Highly deprotonated nanochannel byhydroxide ions (OH⁻) in KOH aqueous solution exhibited highly rectifyingcurrent profile compared to that of HCl. Inset is the surface chargedensity of GO channels evaluated at pH 2.77 and 11.26, respectively.

FIG. 13B is a graph showing pH-dependent variation of the interstitialspacing, obtained from membranes immersed in different pH solutionsusing in-situ AFM analysis.

FIG. 14A is a graph showing current-voltage transport behaviors underasymmetric conditions (10⁻¹ M KCl and varying pH at values of (i) 11.10,(ii) 9.18 and (iii) 6.27 on the feed chamber, and 10⁻² M and constant pHof about 6 on the permeate chamber).

FIG. 14B is a graph showing current-voltage transport behaviors underasymmetric conditions (10⁻¹ M KCl and varying pH at values of (i) 2.7,(ii) 4.0 and (iii) 5.2 on the feed chamber, and 10⁻² M and constant pHof about 6 on the permeate chamber).

FIG. 15 is a schematic diagram showing a graphene oxide nanochannelpresumed as a rectangular channel with dimensions of effective height,h, channel length, L_(channel), and channel width, 2R.

FIG. 16A is a schematic diagram depicting an analytical model with arectangular pore possessing the surface charges on the top andbottom-sheets.

FIG. 16B is a graph showing calculated molarity by applying theparameters: Γ=0.5 nm⁻², R=28 nm, h₀=0.9 nm, δ=1.3 nm, pK=0, pL=6,L_(Channel)=0.4 mm, μ₊=3.1×10⁻⁷ m²/V-s, μ⁻=5.5×10⁻⁸ m²/V-s. Solid linesshow the calculated results from the analytical model, and the filledmarkers in the figure correspond to experimentally obtained data shownin FIG. 12A.

FIG. 16C is a graph showing calculated pH-dependent ionic conductancesby applying the parameters: Γ=0.5 nm⁻², R=28 nm, h₀=0.9 nm, δ=1.3 nm,pK=0, pL=6, Lchannel=0.4 mm, μ₊=3.1×10⁻⁷ m²/V-s, μ⁻=5.5×10⁻⁸ m^(2/V)-s.Solid lines show the calculated results from the analytical model, andthe filled markers in the figure correspond to experimentally obtaineddata shown in FIG. 9D.

FIG. 17A is a schematic diagram depicting an analytical model of acylindrical nanochannel with surface charges on circumference ofcylindrical channel.

FIG. 17B is a graph showing calculated molarity by applying theparameters: Γ=0.5 nm⁻², R_(pore)=0.45 nm, δ=0.1 nm, pK=0, pL=6,L_(pore)=0.05 mm, μ₊=3.1×10⁻⁷ m²/V-s, μ⁻=5.5×10⁻⁸ m²/V-s. Solid linesshow the calculated results from the analytical model, and the filledmarkers in the figure correspond to experimentally obtained data shownin FIG. 12A.

FIG. 17C is a graph showing calculated pH-dependent ionic conductance byapplying the parameters: Γ=0.5 nm⁻², R_(pore)=0.45 nm, δ=0.1 nm, pK=0,pL=6, L_(pore)=0.05 mm, μ₊=3.1×10⁻⁷ m²/V-s, μ⁻=5.5×10⁻⁸ m²/V-s. Solidlines show the calculated results from the analytical model, and thefilled markers in the figure correspond to experimentally obtained datashown in FIG. 9D.

FIG. 18A is a graph showing current-voltage curves measured at differentsalt concentrations at around pH 5.5. Inset shows the rectificationfactor RF as a function of molarity, describing the relative ratio ofthe measured currents at scan voltages of ±80 mV.

FIG. 18B is a graph showing current-voltage curves obtained fromdifferent feed concentrations and the constant concentration gradient ofC_(High)/C_(Low)=10 at pH 5.5. Inset shows the increasing membranepotentials with dilution of the electrolytes (feed molarity c_(F)),associated with the enhancement of the cation selectivity.

FIG. 19A is a schematic diagram of an electrodialysis process accordingto a first configuration. As shown in the figure, anion membranes (“am”)and cation membranes (“cm”) may be formed into a multi-cell arrangementbuilt on a plate-and-frame to form a stack comprising 100 cell pairs orless. A cell pair is marked up in the figure using the dashed box. Thecation membranes and anion membranes are arranged in an alternatingarrangement between the anode and cathode, whereby the membrane that ispositioned nearest to the anode assumes a positive charge while themembrane that is positioned nearest to the cathode assuming a negativecharge. As shown in the figure, anion membranes with fixed positivegroups are able to exclude positive ions, but are permeable tonegatively charged ions. Likewise, cation membranes with fixed negativegroups are able to exclude negatively charged ions, but are permeable topositively charged ions. By passing a liquid reagent containing ionsthrough a space or passageway defined by an anion membrane and a cationmembrane, negatively charged ions and positively charged ions may beseparated from a feed stream by permeating respectively through theanion membrane and the cation membrane, to result in a dilute streamwhere ions have been substantially removed and a concentrate streamcontaining the ions.

FIG. 19B is a schematic diagram of an electrodialysis process accordingto a second configuration. As shown in the figure, anion membranes withfixed positive groups are able to exclude positive ions, but ispermeable to negatively charged ions. Likewise, cation membranes withfixed negative groups are able to exclude negatively charged ions, butis permeable to positively charged ions. By passing a liquid reagentsuch as water containing ions to be separated (“Feed Water”) through aspace or passageway defined by an anion membrane and a cation membrane,negatively charged ions and positively charged ions may be separatedfrom Feed Water by permeating respectively through the anion membraneand the cation membrane. As a result, ultrapure water which is free oressentially free of ions may be obtained.

DETAILED DESCRIPTION

Advantageously, by forming a stacked arrangement of layers of agraphene-based material, wherein the layers of the graphene-basedmaterial define one or more nanochannels between neighboring layers, andvarying an electrical charge on a surface of the layers of thegraphene-based material defining the one or more nanochannels to controlsize selectivity and/or ionic selectivity of the graphene-basedmembrane, improvements in size and/or ion rejection of thegraphene-based membrane may be effected while not affecting its waterflux performance unduly. The membranes disclosed herein may directly beapplied as desalination membranes, nanofiltration membranes,biofiltration membranes, ion-exchange membranes, electrodialysismembranes, and filtration membranes, for use in a myriad of applicationssuch as water purification, and pharmaceutical, chemical and fuelseparation.

With the above in mind, various embodiments refer in a first aspect to amethod of preparing a graphene-based membrane.

The term “membrane” as used herein refers to a semi-permeable materialthat selectively allows certain species to pass through it whileretaining others within or on the material. A membrane thereforefunctions like a filter medium to permit a component separation byselectively controlling passage of the components from one side of themembrane to the other side. Examples of membrane types include hollowfiber membranes, flat-sheet membranes, spiral wound membranes, ortubular membranes. Flat-sheet membranes are formed from one or moresheets of membrane material placed adjacent to or bonded to one another.Spiral wound membranes are flat sheet membranes which are wrapped arounda central collection tube. Tubular membranes and hollow fiber membranesassume the form of hollow tubes of circular cross-section, whereby thewall of the tube functions as the membrane.

The membrane disclosed herein is a graphene-based membrane. As usedherein, the term “graphene-based membrane” refers to a membranecomprising or formed of graphene or a material based on graphene, suchas graphene oxide, reduced graphene oxide, and derivatives of graphene.Examples of derivatives of graphene include chemically functionalizedgraphene sheets, intercalated graphene sheets, and graphene-basedcomposites.

Graphene refers generally to a form of graphitic carbon, in which carbonatoms are covalently bonded to one another to form a two-dimensionalsheet of bonded carbon atoms. The carbon atoms may be bonded to oneanother via sp² bonds, and may form a 6-membered ring as a repeatingunit, and may further include a 5-membered ring and/or a 7-memberedring. In its crystalline form, two or more sheets of graphene may bestacked together to form multiple stacked layers. Generally, the sideends of graphene are saturated with hydrogen atoms.

Graphene oxide refers to oxidized forms of graphene, and may include anoxygen-containing group such as a hydroxyl group, an epoxide group, acarboxyl group, and/or a ketone group. Reduced graphene oxide refers tographene oxide which has been subjected to a reduction process, therebypartially or substantially reducing it. For example, after subjectingthe graphene oxide to a reduction process, some of the oxygen-containinggroups remain in the reduced graphene oxide that is formed. Thereduction process may take place via a chemical route, or by thermaltreatment. By at least partially reducing graphene oxide to form reducedgraphene oxide, while not reducing it to graphene, some of theoxygen-containing groups may be removed from graphene oxide therebypartially restoring the graphene sp² network. In so doing, this allowscharge transfer to take place in the restored graphene network, therebyconferring electrical conductivity to the material.

Chemically functionalized graphene refers to graphene sheets containingchemical functional groups which may be covalently bonded to the basalplane or the edge of the sheets. Such groups may include, but are notlimited to, di-carboxylic acid, organosulfate and/or amino groups. Thechemical functional groups present on the chemically functionalizedgraphene may confer a different functionality to graphene-basedmembranes, such as: (a) ability to control surface charge in thenanochannels to render surface of the nanochannels positively charged ornegatively charged; (b) ability to control height of the nanochannels;and/or (c) ability to enhance structural stability of the graphene-basedmembrane by cross-linking stacked graphene sheets.

Graphene composite refers to a composite formed of graphene sheets withpolymers and/or nanoparticles adsorbed on a surface of the graphenesheets. Examples of polymers that may be used to form the graphenecomposite include, but are not limited to, polysulfone, fibroin,polyaniline, polyamide, poly(ethersulfone), deoxyribonucleic acid,mixtures thereof, and copolymers thereof. Nanoparticles, on the otherhand, may include carbon nanotubes, carbon nanodots, titanium dioxidenanoparticles, and/or gold nanoparticles, to name only a few. Thegraphene sheets with at least one of the polymers or nanoparticles mayinteract with one another or be held in place in the graphene compositevia non-covalent bonding, such as van der Waals bonding, hydrophobicinteraction, pi-stacking, or electrostatic bonding. As in the case forchemically functionalized graphene mentioned above, modifications of thegraphene sheets by forming composites with polymers or withnanoparticles may confer a different functionality to graphene-basedmembranes, such as: (a) ability to control surface charge in thenanochannels to render surface of the nanochannels positively charged ornegatively charged; (b) ability to control height of the nanochannels;and/or (c) enhance structural stability of the graphene-based membraneby cross-linking stacked graphene sheets.

In various embodiments, the graphene-based material comprises graphene,graphene oxide, chemically functionalized graphene, or combinationsthereof. In some embodiments, the graphene-based material comprisesgraphene oxide. In specific embodiments, the graphene-based materialconsist essentially of, or is formed entirely of graphene oxide.

The method comprises providing a stacked arrangement of layers of agraphene-based material. The graphene-based material may, for example,be in the form of a graphene sheet or a graphene-oxide sheet. Each ofthe layers of the graphene-based material may have a lateral dimensionin the range of about 0.1 μm to about 10 μm, such as about 0.5 μm toabout 10 μm, about 1 μm to about 10 μm, about 3 μm to about 10 μm, about5 μm to about 10 μm, about 6 μm to about 10 μm, about 0.1 μm to about 8μm, about 0.1 μm to about 6 μm, about 0.1 μm to about 4 μm, about 1 μmto about 6 μm, about 3 μm to about 9 μm, or about 4 μm to about 8 μm.

By the term “stacked arrangement”, it is meant that at least two layersof the graphene-based material are arranged in proximity to each anothersuch that at least a portion of a surface of the two layers overlap. Theat least two layers of the graphene-based material may be spaced apartby a distance to each other. In so doing, the layers of thegraphene-based material may define one or more nanochannels betweenneighboring layers, wherein the term “nanochannel” as used herein refersto a conduit, channel, or a similar structure having at least onedimension that is at a nanometer scale, and through which a fluid suchas a liquid may pass through.

By forming a stacked arrangement of layers of a graphene-based material,this allows the graphene-based material to function as a membrane. Forexample, the graphene-based membrane may be formed from graphene sheets.Even though the graphene sheets may be impermeable to fluid flowtherethrough, a stacked arrangement of the graphene sheets may defineone or more nanochannels between neighboring layers, through which afluid such as a liquid may pass through.

The cross-sectional width of the one or more nanochannel defined by theneighboring layers of the graphene-based material may depend on orcorrespond to the distance between the neighboring layers. For example,the neighboring layers of the graphene-based material may be spacedapart by a distance in the range of about 0.5 nm to about 2 nm, such asabout 0.8 nm to about 2 nm, about 1 nm to about 2 nm, about 1.5 nm toabout 2 nm, about 0.5 nm to about 1.8 nm, about 0.5 nm to about 1.5 nm,about 0.5 nm to about 1.2 nm, about 0.9 nm to about 1.2 nm, about 0.9 nmto about 1 nm, about 1 nm to about 1.1 nm, or about 0.95 nm to about1.15 nm. Accordingly in various embodiments, each of the one or morenanochannels may have a maximal cross-sectional width in the range ofabout 0.5 nm to about 2 nm, or a maximal cross-sectional widthcorresponding to a spacing distance between the neighboring layers ofthe graphene-based material mentioned above.

In various embodiments, providing the stacked arrangement of layers of agraphene-based material comprises providing a suspension comprisinglayers of the graphene-based material dispersed therein, filtering thesuspension through a porous substrate to dispose the layers of thegraphene-based material as a stacked arrangement on the poroussubstrate, and separating the stacked arrangement of layers of thegraphene-based material from the porous substrate.

Providing the suspension comprising layers of the graphene-basedmaterial dispersed therein may comprise sonicating a dispersioncomprising the graphene-based material to exfoliate the graphene-basedmaterial into layers. As used herein, the term “exfoliate” refers to aprocess by which a layered or stacked structure is transformed to onethat is substantially de-laminated, disordered, and/or no longerstacked. By sonicating a dispersion comprising the graphene-basedmaterial, for example, layers of the graphene-based material, which maybe held together by van der Waals bonding in a layered structure, may beseparated into their individual layers. In so doing, individual layersof the graphene-based material may be at least substantially uniformlydispersed in the suspension.

In order that the suspension may comprise or largely comprise individuallayers or monolayers of the graphene-based material, the methoddisclosed herein may include removing graphene-based material whichremain as multilayer crystals from the dispersion following sonicationto obtain the suspension. This may be carried out, for example, bycentrifuging the dispersion.

The suspension may be filtered through a porous substrate to dispose thelayers of the graphene-based material as a stacked arrangement on theporous substrate. The porous substrate may, for example, be anodiscalumina membrane (AAO), carbon foam, ceramic membrane, or polymericmembranes such as, but not limited to, membranes formed frompolycarbonate (PC), polyvinylidene fluoride (PVDF), polysulfone (PSF),polyacrylonitrile (PAN), polyethersulfone (PES), polytetrafluoroethylene(PTFE), polyamide (PA), mixtures thereof, or copolymers thereof. Toshorten the time for forming the stacked arrangement, a vacuum may beapplied to the porous substrate so as to increase the rate at which thesuspension is being drawn through the porous substrate.

Upon forming the stacked arrangement of layers of the graphene-basedmaterial, the stacked arrangement of layers of the graphene-basedmaterial may be separated from the porous substrate. This may be carriedout, for example, by immersing the porous substrate comprising thestacked arrangement of layers of the graphene-based material disposedthereon in a liquid reagent such as water. In so doing, the stackedarrangement of layers of the graphene-based material may separate fromthe porous substrate, and may float on a surface of the liquid reagentto form a free-standing graphene-based membrane.

In addition to, or apart from the above-mentioned, providing the stackedarrangement of layers of a graphene-based material may be carried out bya deposition technique selected from the group consisting of spraycoating, drop casting, spin-casting, doctor-blade casting,Langmuir-Blodgett, layer-by-layer assembly and combinations thereof.

The stacked arrangement of layers of the graphene-based material may bearranged on a supporting substrate to improve mechanical strength of theresulting membrane. For example, the supporting substrate may be aporous substrate having a porosity and/or pore size that does not affectliquid flux through the graphene-based membrane.

In various embodiments, the supporting substrate is a membrane formed ofa material selected from the group consisting of SiN_(x), carbon foam,ceramic membrane, and polymeric membrane. Examples of a polymericmembrane that may be used include, but are not limited to, polycarbonate(PC), polyvinylidene fluoride (PVDF), polysulfone (PSF),polyacrylonitrile (PAN), polyethersulfone (PES), polytetrafluoroethylene(PTFE), and polyamide (PA). In some embodiments, the supportingsubstrate is a membrane formed of SiN_(x).

In some embodiments, the membrane of the supporting substrate comprisesan array of nanopores. By limiting the exposed membrane area to a smallarea such as 2.5 μm² or less, while keeping the graphene-based membranerelatively thick, it may avoid degradation of the graphene-basedmembrane due to unintended cracks and defects.

In various embodiments, the stacked arrangement of layers of thegraphene-based material may be configured such that the resultantgraphene-based membrane assume different geometries, such as hollowfiber membranes, flat-sheet membranes, spiral wound membranes, ortubular membranes. In the case of a hollow fiber membrane, for example,the stacked arrangement of layers of the graphene-based material may bearranged on a cylindrical supporting substrate, so that a hollow fibermembrane is obtained.

The method of preparing a graphene-based membrane disclosed hereinfurther comprises varying an electrical charge on a surface of thelayers of the graphene-based material defining the one or morenanochannels to control size selectivity and/or ionic selectivity of thegraphene-based membrane.

In various embodiments, varying an electrical charge on a surface of thelayers of the graphene-based material defining the one or morenanochannels comprises at least one of (i) varying polarity of theelectrical charge; (ii) varying magnitude of the electrical charge, or(iii) arranging layers of opposite electrical charges in the stackedarrangement.

For example, varying polarity of the electrical charge on a surface ofthe layers of the graphene-based material defining the one or morenanochannels may involve converting negatively charged surface groupssuch as carboxyl groups, —SO³⁻, and/or hydroxyl groups that may bepresent on a surface of the graphene-based material to positivelycharged surface groups such as amino groups and/or trialkylammoniumgroups. One example by which this may be carried out is amide synthesisfrom carboxylic acid via carbodiimide-mediated amidation. In so doing,rejection rate of the graphene-based membrane to cations over that ofanions may be increased.

Varying magnitude of the electrical charge on a surface of the layers ofthe graphene-based material defining the one or more nanochannels mayinvolve increasing magnitude of the electrical charge. This may allowanion/cation selectivity and selectivity based on ionic valence to beincreased. Advantageously, ion rejections may be increased, whileretaining size-selected permeation of neutral molecular species.

Arranging layers of opposite electrical charges in the stackedarrangement may comprise interlaying positively and negatively chargedlayers of the graphene-based material in the stacked arrangement. In sodoing, a tandem structure of negatively and positively charged layers ofthe graphene-based material may result. Size-cutoff for both anions andcations has been found by the inventors to increase significantlywithout lowering water permeability that may otherwise result fromchanging size of nanochannels within the membrane.

The above-mentioned ways in which an electrical charge on a surface ofthe layers of the graphene-based material defining the one or morenanochannels is varied may be carried out by at least one of (i) achemical substitution process on the graphene-based material, (ii) areduction process on the graphene-based material, which may be carriedout chemically and/or thermally, or (iii) contacting the graphene-basedmaterial with a liquid reagent and varying molarity and/or pH of theliquid reagent.

For example, varying an electrical charge on a surface of the layers ofthe graphene-based material defining the one or more nanochannels by achemical substitution process on the graphene-based material may involvesynthesis of amide from carboxylic acid via carbodiimide. Contacting thegraphene-based material with a liquid reagent and varying molarityand/or pH of the liquid reagent, on the other hand, may involveprotonation or deprotonation of carboxyl or hydroxyl groups, which maytake place depending on pH of the liquid reagent.

In various embodiments, the method of preparing a graphene-basedmembrane disclosed herein further comprises applying pressure to asurface of the stacked arrangement of layers of the graphene-basedmaterial. This may be carried out, for example, by applying a fluid suchas a gas or a liquid under application of a force to the surface of thestacked arrangement of layers of the graphene-based material.Compression of the nanochannels within the graphene-based membrane maytake place as a result. As the charged surfaces of the layers of thegraphene-based material defining the one or more nanochannels approacheach other, electrostatic repulsion force between the layers mayincrease, leading to increase in ionic selectivity performance of thegraphene-based membrane.

From the above discussion, it may be seen that size selectivity and/orionic selectivity of the graphene-based membrane may be controlled byvarying an electrical charge on a surface of the layers of thegraphene-based material defining the one or more nanochannels.

As used herein, the term “selectivity” refers to a permeation ratiobetween components in a feed stream. Accordingly, the term “sizeselectivity refers to selectivity derived from a difference in size ofthe components, while the term “ionic selectivity” refers to selectivityderived from a difference in electrical charge of the components, andmay be expressed as a ratio of permeability of positively charged andnegatively charged ions. The respective selectivity may be used asperformance indicators of a membrane, for example, where species of acertain size, or only certain ionic species may pass through themembrane.

Advantageously, a graphene-based membrane according to embodimentsdisclosed herein have demonstrated good ionic selectivity for separationof K⁺ and Cl⁻ ions. In various embodiments, the graphene-based membranedisclosed herein is configured to reject ions having a radius ofhydration of at least about 4.5 Å.

Various embodiments refer in a second aspect to a graphene-basedmembrane comprising a stacked arrangement of layers of a graphene-basedmaterial. Suitable graphene-based materials have already been mentionedabove. In various embodiments, the graphene-based material comprisesgraphene oxide.

The graphene-based material may, for example, be in the form of agraphene sheet or a graphene-oxide sheet. Each of the layers of thegraphene-based material may have a lateral dimension in the range ofabout 0.1 μm to about 10 μm, such as about 0.5 μm to about 10 μm, about1 μm to about 10 μm, about 3 μm to about 10 μm, about 5 μm to about 10μm, about 6 μm to about 10 μm, about 0.1 μm to about 8 μm, about 0.1 μmto about 6 μm, about 0.1 μm to about 4 μm, about 1 μm to about 6 μm,about 3 μm to about 9 μm, or about 4 μm to about 8 μm.

The layers of the graphene-based material define one or morenanochannels between neighboring layers. As mentioned above, theneighboring layers of the graphene-based material may be spaced apart bya distance in the range of about 0.5 nm to about 2 nm. In view that thelayers of the graphene-based material define one or more nanochannelsbetween neighboring layers, the spacing between the neighboring layersmay correspond to a maximal cross-sectional width of the one or morenanochannels.

A surface of the layers of the graphene-based material defining the oneor more nanochannels possess an electrical charge, wherein the layers ofthe graphene-based material are configured to control size selectivityand/or ionic selectivity of the graphene-based membrane by varying theelectrical charge.

In various embodiments, the layers of the graphene-based material areconfigured to control size and/or ionic selectivity of thegraphene-based membrane by varying at least one of (i) polarity of theelectrical charge; (ii) magnitude of the electrical charge, or (iii)arranging layers of opposite electrical charges in the stackedarrangement. Specific methods by which the electrical charge may bevaried to control size selectivity and/or ionic selectivity of thegraphene-based membrane have already been discussed above.

In various embodiments, the graphene-based membrane disclosed herein isconfigured to reject ions having a radius of hydration of at least about4.5 Å.

In some embodiments, the stacked arrangement of layers of agraphene-based material is arranged on a supporting substrate. Suitablematerials that may be used as the supporting substrate have already beenmentioned above. In specific embodiments, the supporting substrate is afurther membrane, such as a membrane formed of SiN_(x), comprising anarray of nanopores.

As mentioned above, in addition to flat-sheet membranes, thegraphene-based membrane may also assume different geometries, such ashollow fiber membranes, spiral wound membranes, or tubular membranes.

The graphene-based membrane disclosed herein may directly be applied asdesalination membranes, nanofiltration membranes, biofiltrationmembranes, ion-exchange membranes, electrodialysis membranes, andfiltration membranes, to name only a few, for use in a myriad ofapplications such as water purification, and pharmaceutical, chemicaland fuel separation.

For example, the graphene-based membrane disclosed herein is able toincrease ionic rejection rate without lowering water flux, therebyrendering it suitable for use in reverse osmosis water desalinationapplications. As further examples, the membranes disclosed herein aresuitable for use in nanofiltration, as ionic and molecular selectivityof the membranes may be improved while retaining the ultra-high waterflux of graphene oxide membranes. Advantageously, chemical inertness ofthe graphene-based membrane disclosed herein means that the membranesdisclosed herein are suitable for biofiltration. The large ionicselectivity values also means that the membranes are conducive forelectrodialysis application and as ion-exchange membranes.

In line with the above, various embodiments refer in a further aspect toa method of separating ions from a fluid stream. The method comprisesproviding a graphene-based membrane prepared by a method according tothe first aspect or a graphene-based membrane according to the secondaspect, and directing a fluid stream comprising one or more ions towardsa first surface of the graphene-based membrane, wherein ions to beseparated from the fluid stream are filtered through the graphene-basedmembrane. In various embodiments, directing the fluid stream comprisingone or more ions towards a first surface of the graphene-based membraneis carried out without an electrical field. For example, pressure may beused as the driving force for directing fluid stream to thegraphene-based membrane.

In some embodiments, directing the fluid stream comprising one or moreions towards a first surface of the graphene-based membrane is carriedout with an electrical field. The method of separating ions from a fluidstream, where directing the fluid stream comprising one or more ionstowards a first surface of the graphene-based membrane is carried outwith an electrical field may, for example, be applied toelectrodialysis.

As used herein, the term “electrodialysis” refers to a electrochemicalprocess involving use of at least one ion-selective or ion exchangemembrane, whereby ions are transported through the at least oneion-selective or ion exchange membrane from one solution to anotherunder driving force of an electrical potential difference such as thatshown in FIG. 19A and FIG. 19B. In so doing, removal or separation ofelectrolytes may be achieved by electrodialysis.

With the above in mind, two or more graphene-based membranes prepared bya method according to the first aspect or a graphene-based membraneaccording to the second aspect may be arranged to form a cell ormulti-cell arrangement such as that shown in FIG. 19A. A fluid streamcomprising one or more ions may be directed towards a first surface ofthe graphene-based membranes by, for example, directing the fluid streaminto a passageway defined by two membranes. Ions to be separated fromthe fluid stream may then be separated or removed from the fluid streamby filtering through the graphene-based membranes.

Advantageously, the graphene-based membrane according to embodimentsdisclosed may be used in or applied to electrodialysis, as they havedemonstrated enhanced ionic selectivity in their abilities toselectively transport ions having positive or negative charge and rejections of the opposite charge.

The invention has been described broadly and generically herein. Each ofthe narrower species and subgeneric groupings falling within the genericdisclosure also form part of the invention. This includes the genericdescription of the invention with a proviso or negative limitationremoving any subject matter from the genus, regardless of whether or notthe excised material is specifically recited herein.

Other embodiments are within the following claims and non-limitingexamples. In addition, where features or aspects of the invention aredescribed in terms of Markush groups, those skilled in the art willrecognize that the invention is also thereby described in terms of anyindividual member or subgroup of members of the Markush group.

EXPERIMENTAL SECTION

Herein, various embodiments refer to a material for separation of ionsfrom a fluid stream, comprising one or more graphene-based selectivelayers which may be intrinsically charged. The selective layers may havethe same or different charges, and these charges may be positive ornegative. The material may optionally be supported on a substrate toimprove the overall mechanical strength of the structure. The materialmentioned herein may refer to membranes or other materials that may beused for the purpose of this technology.

Various embodiments also relate to a method for separating ions from afluid stream, comprising (i) providing materials with charged selectivelayers that are graphene based and with apertures dimensioned to allowflow of desired fluid molecules, and (ii) contacting fluid stream with afirst surface of the charged material under suitable driving force toreject ions and allow desired fluid molecules to pass through to thesecond surface, wherein the driving force does not involve the use of anelectrical field.

Various embodiments further refer to a method for significantlyincreasing and tuning the ionic rejection rate and ionic selectivity inlamellar graphene oxide membranes. The method may be applied tomembranes, such as nanofiltration membranes, desalination membranes,biofiltration membranes, and ion-exchange membranes.

In greater detail, lamellar nanoporous membranes made from grapheneoxide (GO) nanosheets have an ultra-high water flux (1000 better thancurrent membranes), and show a sharp size cutoff at about 4.5 Å in ionicpermeability as a function of hydrated radii of the permeant ions ororganic molecules. Ionic rejection may be driven by geometric sizeexclusion, and size of nanochannels in GO membranes may be decreased toachieve a much smaller cutoff size required for desalination.

As identified herein, there is presence of an important additionalmechanism that defines ionic permeability in GO membranes: chargesurface groups inside the GO nanochannels are responsible forelectrostatically repulsing co-ions. For example, it was found by theinventors that negatively charged GO membranes have 10 times smallerpermeability for negatively charged Cl⁻ ions and for positively chargeK⁺ ions, although they have the same hydration radius. The same trend isobserved for many other ionic species, as discussed below.

By chemically engineering the charged surface groups within GO-derivedlaminates of the membrane, ionic selectivity and size cutoff ofGO-derived membranes may be increased. This may involve one or more of(a) converting negatively charged surface group to positively chargedsurface groups; (b) increasing magnitude of the surface charge; and (c)interlaying positively and negatively charge GO-derived laminates withinthe membrane.

By converting negatively charged surface groups to positively chargedsurface groups, cation rejection rate over anion may be increased.

By increasing magnitude of the surface charge, anion/cation selectivityand selectivity based on ionic valence may be increased. Ion rejectionsmay be increased, while retaining size-selected permeation of neutralmolecular species.

By interlaying positively and negatively charge GO-derived laminateswithin the membrane, size-cutoff for both anions and cations may beincreased significantly without lowering water permeability that mayotherwise result from changing size of nanochannels within the membrane.The tandem structures of negatively and positively charged grapheneoxide sheets allow electrostatic water desalination to take place.

Surface charge-driven ion sieving properties of membranes disclosedherein may result from charged graphene oxide capillaries, which leadsto high rejection levels of like-charge ions in the capillary.Advantageously, the increase in ion rejection via surface chargemodulation may be effected without affecting the excellent waterpermeation properties of the GO-derived membranes. Further, the chargeson the membrane surface is tunable by varying molarities or pH ofelectrolytes. Chemical substitution or reduction processes may becarried out to control the charges. These translate into tunable,surface charge-governed ion permselectivity characteristics of themembranes disclosed herein.

The membranes disclosed herein may directly be applied as desalinationmembranes, nanofiltration membranes, biofiltration membranes,ion-exchange membranes, electrodialysis membranes, and filtrationmembranes, for use in a myriad of applications such as waterpurification, and pharmaceutical, chemical and fuel separation.

For example, although state of the art GO membranes may have ultra-highwater flux, their ionic rejection rate is insufficient for reverseosmosis water desalination applications. The engineered GO membranesdisclosed herein is able to increase ionic rejection rate withoutlowering water flux, thereby rendering it suitable for use in reverseosmosis water desalination applications.

As further examples, the membranes disclosed herein are suitable for usein nanofiltration, as ionic and molecular selectivity of the membranesare improved while retaining the ultra-high water flux of GO membranes.Advantageously, chemical inertness of GO membranes means that themembranes disclosed herein are suitable for biofiltration. The largeionic selectivity values also means that the membranes are conducive forelectrodialysis application and as ion-exchange membranes.

Example 1: Microscopic Graphene Oxide Membranes and Demonstration of itsIonic Charge Selectivity Example 1-A: Fabrication of Freestanding SiNxMembrane and Nanopore Arrays

As a supporting substrate for graphene oxide (GO) membranes, a 3×3 mm²Si/SiN_(X) chip with free-standing SiN_(X) membrane perforated with anarray of nanopores was used.

The support chip was fabricated from a standard 4-inch silicon wafer,coated from both sides with a 300 nm thick low-stress SiN_(X) layerdeposited at Cornell NanoScale Science and Technology Facility, usinglow pressure chemical vapor deposition. Photolithography and reactiveion etching were used to define windows in the SiN_(x) coating on oneside of the support chip.

Using standard isotropic wet chemical etching with potassium hydroxide(KOH), through the windows, 150×150 μm² sized freestanding membranes ofSiN_(X) having a thickness of 300 nm were fabricated.

The processed silicon wafer was subsequently diced into 3×3 mm² chips,with a freestanding membrane in the center of each chip. In the centerof the freestanding membrane, direct milling using Ga-source focused ionbeam (FIB) microscopy (AURIGA 60, Carl ZEISS Microscopy, GmBH; HeliosNanoLab DualBeam, FEI Company) was used to fabricate a 12×12 array ofsquare-shaped nanopores with dimensions 200×200 nm² spaced 200 nm apart.

Example 1-B: Fabrication of Graphene Oxide Membranes

Graphite oxide was prepared by the modified Hummers method, andexfoliated into monolayer sheets by sonication in deionized water,following by centrifugation at 5,000 g to remove remaining multilayercrystals. GO membranes were prepared by the vacuum filtration of the GOsuspension through Anodisc Alumina (AAO) membranes with a pore size of0.02 μm, and had thicknesses of between 10 nm to 10 μm depending on theconcentration of GO suspension.

The GO membrane was dried overnight at ambient conditions. Separation ofthe GO membranes from AAO filters was achieved by immersing in water,whereby the GO membranes spontaneously floated on the water surface whenimmersed in water while the AAO filters sank down the bottom.

The freestanding GO membranes floating on water surface was scooped ontothe silicon chip with a small area of suspended SiN_(x). Thechip-mounted GO membranes were fully dried overnight at ambientconditions.

Example 1-C: Fluidic Cell Preparation

The chip-mounted GO membranes were assembled between two half-cells of acustom-built microfluidic cassette made of polyether-ether-ketone. Thetwo sides of the chips were sealed with polydimethylsiloxane (PDMS)gaskets, with openings to the supported GO membrane from each side. Thechambers of each half-cell were filled with an electrolyte of choice andput into contact with Ag/AgCl electrodes.

Example 1-D: Ion Transport Measurements

The Ag/AgCl electrodes in each half-cell were used to apply an electricpotential across the graphene oxide membranes and to measure ioniccurrents. The current were acquired using an Axopatch 200B (AxonInstruments) amplifier, which was connected to a low-noise dataacquisition system, Digidata 1440A (Axon Instruments). The ionicconductance of the membrane was calculated from the slope of the I-Vcurve at low voltage (−10 mV to +10 mV).

Example 1-E: Characterizations of Graphene Oxide Membranes

Physiochemical properties of the graphene oxide nanosheets wereinvestigated using AFM, atomic force microscopy (Cypher, OxfordInstruments and Dimension_Fastscan, Bruker) and FTIR, Fourier transforminfrared spectroscopy (Vertex 80v, Bruker). In addition, X-ray powderdiffraction (X'Pert, Philips) data were collected with λCuKα radiationusing a conventional diffractometer. The experimental conditions were:Bragg Brentano geometry, fixed divergence and receiving slits, step scanmode in the range of 5°<2θ<45° with 2θ=0.02° and t=3 s counting time.

Example 1-F: Experimental Results on Ionic Selective Transport

To elucidate the ionic selectivity of the GO membranes, the permeabilityof a wide selection of aqueous salt ions, with varying ionic charges andspanning a wide range of effective hydrated ionic volume wereinvestigated (FIG. 2A).

From the evaluated permeation rates, two general trends were revealed:(a) cation permeability decreased exponentially with increased hydrationradius, followed by the sharp cutoff at R_(H)≈4.6 Å; and (b)permeability of the negatively charged Cl⁻ ion was suppressed by anorder of magnitude compared to the positive K⁺ and Rb⁺ ions, despite allthose ions having very similar hydration volumes.

For example, potassium chloride exhibited the highly selective,cation-to-anion permeability ratio (P⁺/P⁻) of up to max 10 as shown inFIG. 2B. This selectivity was a result from the expulsion of thenegatively charged Cl⁻ ions from nanochannels, and suppression of theanionic permeability, as predicted by the electric double layer model.Permeability of Cl⁻ ions in monovalent salts remained independent ofcounterions (Rb⁺, K⁺, Na⁺, Li⁺); and the cation selectivity, P⁺/(P⁺+P⁻)reached values in excess of 90%.

Example 2: Water Permeance Across Scaled-Up Graphene Oxide MembranesExample 2-A: Fabrication of Scaled-Up Graphene Oxide Membranes and WaterPermeance Measurements

The graphite oxides were exfoliated into monolayer sheets by sonicationin deionized water, following by centrifugation at 5,000 g to removeremaining multilayer crystals. GO membranes were prepared by the vacuumfiltration of the GO suspension through Anodisc Alumina (AAO) membraneswith a pore size of 0.02 μm and had thicknesses of between 0.3 to 3 μmdepending on the concentration of GO suspension.

Water flux evaluation was performed on a dead end filtration device(HP4750 Stirred Cell, Sterlitech Corp.) The transmembrane pressure isdriven by nitrogen gas in the range of 1 to 7 bars. The effective area(A) of water permeation in the cell is 8.295 cm². The membranes sealedby rubber O-ring were fixed at the bottom of the water cell. The waterflux (J) was measured by collecting permeated water (V) across themembranes under certain pressure and calculated using the equationJ=V/A·t·ΔP where t is the operation duration. The water flux wasrecorded when it is stabilized at 1 to 2 bar and neutral pH.

Example 2-B: Experimental Results on Water Permeance

As shown in FIG. 4A, water flux at the first pressure loading increasedquickly in low-pressure range, and the increment slowed down under highpressure regime. At high pressure, corrugated ripple in the GO membranesbegan to collapse, leading to the compression of the interlayer channelswith the increasing pressure. As negatively charged GO sheets approachedeach other much closer, the electrostatic repulsion force betweennanosheets increased sharply, leading to the increment of ionicselectivity performances of the GO membranes. When the pressureincreased from 1 bar to 7 bar, the unit water flux at each pressurebecame obviously slower as shown in FIG. 4B. Furthermore, the secondpressure loading was carried out after releasing the applied pressure inorder to ensure sufficient mechanical durability at the pressure wherethe membranes would be used (FIG. 4C). No mechanical crack ordelamination were observed even after iteration.

Example 3: Commercial Feasibility of Graphene Oxide Stacks as IonExchange Membranes

FIG. 5 illustrates that graphene oxide membranes possess commerciallyfeasible performances compared to those from commercial polymeric ionexchange membranes. In particular, the GO membrane can realize ultrahighwater flux exceeding that of polymeric membranes at much thinnerthickness by two order of magnitude while sustaining high ionicpermselectivity.

Example 4: Drift-Diffusion Technique

Using microscopic drift-diffusion experiments over a wide range of ionsof different size and charge, the inventors were able to clearlydisentangle different physical mechanism contributing to the ionicsieving in GO membranes—electrostatic repulsion between ions and chargedchemical groups; and the compression of the ionic hydration shell withinthe membrane's nanochannels, following the activated behavior.

The charge-selectivity allowed for design of membranes with increasedionic rejection, and opened up the field of ion exchange andelectrodialysis to the GO membranes.

The GO membranes consisted of stacked layers of impermeable graphenesheets, where L=1 to 10 μm in size, spaced by d=0.9 to 1.2 nm viafunctionalized, mostly oxygen-carrying groups. The chemical groups werecoalesced into nanoscale domains, delimiting a percolative network ofpristine graphene channels, which could accommodate a few layers ofwater exhibiting frictionless flow.

Previous experiments measuring salt diffusion through centimeter-scalemembranes over a period of hours, showed no permeation for ions withhydration rates above size cut-off of R_(H)≈4.5 Å and mostly unvaryingpermeation rate for smaller ions. The experiments, due to their nature,were (i) ineffective in disentangling all the physical mechanismscontributing to the permeability, (ii) unable to distinguishpermeability of different constituting ions in the salt, and (iii) maybe prone to artifacts due to external defects and tears over largerareas of the membrane.

To understand intrinsic membrane properties, the inventors implemented ahighly sensitive drift-diffusion technique, which revealed ultra-highcharge-selectivity of the GO membranes.

The ionic permeability of a 3 μm thick GO membrane, mounted across anarray of 200×200 nm² apertures in a 300 nm thick, free-standing,insulating SiN_(X) layer on a Si substrate chip was measured (FIG. 6A).By limiting the exposed membrane area to about 5 nm² and keeping itrelatively thick, the inventors ensured there were no unintended cracksand defects that may skew the results. The GO membrane and itsconstituting GO crystallites were extensively characterized usingcharacterization tools such as atomic force microscopy, X-raydiffraction, and Fourier transform infrared spectroscopy (See Example5).

The membrane chip was inserted in a fluidic cell, so that it separatedtwo compartments, each subsequently filled with ionic solutionselectrically contacted with Ag/AgCl electrodes. The electrodes wereconnected to a sensitive patch-clamp amplifier (Axopatch 200B), sourcingvoltage across the membrane and measuring ionic currents with 10 pAprecision. The polydimethylsiloxane (PDMS) gasket seal precluded ionicsolution from leaking around the edges of the membrane.

To discern the separate permeabilities of cations (P₊) and anions (P⁻)in the salt, the inventors implemented the drift-diffusion technique tomeasure ionic currents driven by both the voltage and the concentrationgradient. The fluidic compartments were filled with differentconcentrations of a salt, and the inventors were able to measurediffusive current across the membrane for zero applied voltage using theequation I_(diff)˜(P₊−P⁻)·Δc (FIG. 6B).

As the inventors applied a voltage difference ΔV across the membrane,the added electrophoretic component to the overall current was isI_(drift) (P₊+P⁻)·ΔV (FIG. 6C). Measuring the two current components,both P₊ and P⁻ permeabilities may be deduced.

FIG. 6D shows representative current-voltage (I-V) curves, measured at afixed concentration gradient: the slope of the curve was indicative ofI_(drift); whereas membrane potential V_(m)=V (I=0) is indicative ofI_(diff) More precisely, the inventors extracted the individualpermeabilities by modeling the total current density J(Δc, ΔV) acrossthe membrane using the equation:

$J = {\sum_{S}{P_{S}{z_{S}^{2} \cdot \frac{{F^{2} \cdot \Delta}\; V}{RT} \cdot \frac{\lbrack S\rbrack_{f} - {\lbrack S\rbrack_{p}{\exp \left( \frac{z_{S}{F \cdot \Delta}\; V}{RT} \right)}}}{1 - {\exp \left( \frac{z_{S}{F \cdot \Delta}\; V}{RT} \right)}}}}}$

For each ionic species S in the solution, P_(S) is membranepermeability, z_(S) is the valence, and [S]_(f) and [S]_(p) are theionic concentrations in the feed and permeate chambers, respectively.Potential across the membrane ΔV was adjusted for the electrodes' redoxpotential; R is the universal gas constant; F is Faraday's constant; andT is the temperature. Details on the model and the method are detailedin a subsequent example.

To elucidate the ionic selectivity of the GO membranes, the inventorsinvestigated the permeability of a wide selection of aqueous salt ions,with varying ionic charges and spanning a wide range of effectivehydrated ionic volumes.

FIG. 7A depicts the permeation rates (p) of different cations (circle)and their corresponding Cl⁻ counter ions (squares) as a function of thecation's hydration radii. Two general trends were revealed: (a) cationpermeability decreased exponentially with increased hydration radius,followed by the sharp cutoff at R_(H)≈4.6 Å; and (b) permeability of thenegatively charged Cl⁻ ion was suppressed by an order of magnitudecompared to the positive K⁺ and Rb⁺ ions, despite all those ions havingvery similar hydration volumes. The inventors concluded that the twodominant mechanisms for the ion rejection in GO membranes were sizeexclusion due to compression of the ionic hydration shell in narrowchannels, and electrostatic repulsion due to membrane surface charge(FIG. 7B and FIG. 7C).

The results from earlier diffusion experiments were limited to measuringthe permeability of the least permeable species in a salt—for monovalentsalts they were actually measuring permeability of the chlorinecounter-ion, not cations. This led to apparent size-independentpermeability for ions with hydration radii below the cut-off sizedefined by the channel height (implying rigid hydration shells aroundions).

Instead, by properly separating cations and anions, the inventorsobserved the exponential dependence of the permeability on an ion'shydration radius, consistent with the compressible hydration shellmodel, where coordinated water molecules could rearrange themselves tosqueeze the hydration shell through a narrow channel.

The inventors postulated that the high charge selectivity of the GOmembranes was a result of the negatively charged nanochannels in a GOmembrane, due to the protonable oxygen groups. This led to the expulsionof the negatively charged Cl⁻ ions from nanochannels, and suppression ofthe anionic permeability, as predicted by the electric double layer(EDL) model. Permeability of Cl⁻ ions in monovalent salts remainedindependent of counterions (Rb⁺, K⁺, Na⁺, Li⁺); and the cationselectivity S₊=P₊/(P₊+P⁻); reached values in excess of 95% (FIG. 8).Interestingly, the EDL model does not appear to work in the case ofchloride salts with divalent and trivalent cations, and P(Cl⁻) revertsto the value predicted for uncharged channels (FIG. 7A and FIG. 7D). Theinventors attributed this effect to correlation-induced chargeinversion, where multivalent ions overcompensate monovalent surfacegroups, leading to a sharp drop in, or even an inversion, of theeffective surface charge, which were similarly observed in highlycharged protein channels, such as bacterial porin OmpF, and in narrowsilica channels.

To further investigate the ionic selectivity of GO membranes, theinventors performed a series of drift-diffusion and ionic conductivitymeasurements using KCl aqueous solutions for a range of pH and molarityvalues. FIG. 9A shows current-voltage (I-V) curves for an isotropic KClconcentration c_(KCl)=10 mM, measured for different pH values (see alsoFIG. 12A). The ionic conductance of the membrane was calculated from theslopes of the I-V curves in the Ohmic regime at low voltage. Theincrease in pH (reduction in hydronium concentration) led to increaseddissociation of the carboxyl and hydroxyl groups within the GO sheets:

Graphene-OH

Graphene-O⁻+H⁺

This led to an increase in negative surface charge density in thegraphene nanochannels, and was reflected in an increased conductance andcurrent rectification. At higher pH, the inventors also observed anincrease in P(K⁺), a decrease in P(Cl⁻) and an increase in cationselectivity S+(FIG. 9C), all consistent with the increase in thenanochannels' charge.

The strong surface charge effects were revealed in the membrane'sconductance G₀ variation with the electrolyte concentration c (FIG. 9D).Starting from c=1 M, the observed G₀ immediately deviates from theexpected linear regime for a charge-neutral membrane (black solid line),indicating the compression of the EDL in the nanochannels even at highionic strengths. In contrast, the charge effects were previouslyobserved to dominate the conductance in solid-state constrictions onlyat much lower salt concentrations. The inventors noted that the cationselectivity, as deduced from ionic permeabilities (FIG. 9E), could reachas high a value as S+=96% at low salt concentration (FIG. 9F).

To gain insight into the surface charge-driven ionic transport, theinventors applied mean-field theoretical model based on thePoisson-Boltzmann, Navier-Stokes and Behriens-Grier equations (seeExample 11 below for more details). The model fit the observed pH andmolarity dependence of both the conductivity and the charge selectivitywell (FIG. 9A to FIG. 9F), assuming the ions flow in pristine graphenenanochannels with an effective height of h_(G)=0.9 nm, an effectivewidth in the range of w_(G)˜50 nm, and a linear charge density on thesidewalls corresponding to one protonable charged site per 2 nm (FIG.15). A crucial assumption of the model was the infinite-slip boundarycondition for the water flow at the top and bottom graphene surfaces,and no-slip condition at the oxidized sidewalls. The large slip-lengthwas consistent with the effect of frictionless water flow, as reportedin GO membranes. The other possible geometries could not replicate theobserved pH and molarity dependence of the conductance (see Example 12below).

The inventors employed the same set of parameters to concurrentlysimulate all the independent experiments. Although this continuous-mediamodel may demonstrate a limited scope at nanometer length scales, it wasshown to capture the relevant physics and to give sufficientsemi-quantitative insight, while intermolecular and steric interactionswere renormalized into the effective hydrodynamic dimensions.

In conclusion, the inventors have shown that the ion-rejection ingraphene-oxide membranes was driven as much by the electrostaticrepulsion (defined by the nanochannel surface charge) as it was by theactivated size-exclusion (defined by the nanochannel height). Hence, theengineering of the surface charge of the membrane offered a new venuefor increasing the overall salt rejection, without constraining thewater flux.

The inventors have demonstrated that the GO membranes exhibit ultra-highcharge selectivity, reaching up to 96%, driven by the negative surfacecharge of the oxygen-carrying functional groups in the membrane'snanochannels. Coupled with their high durability and scalability, the GOmembranes were well positioned for applications in high-performance ionexchange and electrodialysis technologies.

Example 5: Physiochemical Characterizations of Graphene Oxide Nanosheets

As mentioned above, the GO membrane and its constituting GO crystalliteswere extensively characterized using characterization tools such asatomic force microscopy, X-ray diffraction, and Fourier transforminfrared spectroscopy.

FIG. 10A is an atomic force microscopy (AFM) map and height profile formonolayer GO nanosheet. (Dimension Fastscan, Bruker) Two-dimensional GOnanosheets at ambient conditions were about 1 nm thick with mean planarwidth of 1 μm.

FIG. 10B is a graph showing Fourier Transform Infrared spectrum (FTIR)of air-dried GO laminates, displaying diverse functionalities such as(C—O) epoxy at 1260 cm⁻¹, (O—H) or C—O Carboxy at 1390 cm⁻¹, (C═O)Carbonyl and Carboxyl at 1718 cm⁻¹, and O—H hydroxyl at 3431 cm⁻¹.

FIG. 11A is a graph showing X-ray diffraction (XRD) spectra comparisonof dried and wet GO films. The inter-plane distance of GO reflection(100), was determined from a Rietveld refinement using conventional XRDdata and program GSAS. Using the space group P6/mmm, a Rietveldrefinement was performed with program GSAS (General Structure AnalysisSystem) until discordance factors R_(wp)=7.00%, R_(p)=5.46%,R_(Bragg)=6.33% and χ²=1.138 2. The obtained cell parameters werea=b=10.517(3) Å and c=1.9(1) Å. The investigated interlayer spacing ofdried and wet GO by XRD was around 8.5754 Å and 12.1615 Å, respectively.

FIG. 11B is a graph showing respective height profile of dried and wetGO films, measured by in situ liquid AFM showing similar increase ininterlayer spacing after wetting.

Example 6: Quantitative Analysis of Ion Selectivity Across the Membranes

To describe ionic transport across the membrane, driven by voltage andconcentration gradients, the inventors assumed that ions moved acrossthe membrane independently and that the electric potential droppedlinearly across the membrane. Using Boltzmann-Planck framework, theinventors derived so called Goldman-Hodgkin-Katz equations, connectingthe current density J and membrane potential V_(m) to the concentrationand voltage gradient across the membrane:

$\begin{matrix}{{J^{(n)} = {P_{(n)}z_{(n)}^{2}\frac{F^{2}\Delta \; V}{RT}\frac{\left( {\left\lbrack S^{(n)} \right\rbrack_{f} - {\left\lbrack S^{(n)} \right\rbrack_{p}{\exp \left( \frac{z_{(n)}F\; \Delta \; V}{RT} \right)}}} \right)}{1 - {\exp \left( \frac{z_{s}F\; \Delta \; v}{RT} \right)}}}},} & (1) \\{{J_{total} = {J^{+} + J^{-}}},} & (2) \\{{V_{m} = {\frac{RT}{p}\ln \frac{\left\lbrack S^{+} \right\rbrack_{f} + {\left( \frac{P_{-}}{P_{+}} \right)\left\lbrack S^{-} \right\rbrack}_{p}}{\left\lbrack S^{+} \right\rbrack_{p} + {\left( \frac{P_{-}}{P_{+}} \right)\left\lbrack S^{-} \right\rbrack}_{f}}}},} & (3)\end{matrix}$

where J^((n)) is ionic current density for cations (n=+), and anions(n=−), and J_(total) is the total current density across the membrane.P_((n)) is membrane permeability and z_((n)) is the valence for eachionic specie n. [S^((n))]_(f) and [S^((n))]_(p) are ionic concentrationsin the feed and permeate chambers, respectively. ΔV is the appliedvoltage, V_(m) is the membrane potential, R is the universal gasconstant (8.314 J-K⁻¹·mol⁻¹), F=9.6485×10⁴ C·mol⁻¹ is Faraday'sconstant, T is the temperature.

The inventors were able to directly deduce the permeability ratio of theions (and ion selectivity) from the membrane potential V_(m). Theinventors first measured the zero current potential V_(c), the potentialfor which the total current through the membrane is zero. Subsequently,the membrane potential may be calculated by subtracting from V_(c) theredox potential V_(redox):

V _(m) =V _(C) −V _(redox)  (4)

The redox potential arose from the unequal chloride concentration at thetwo Ag/AgCl electrodes, and it gave the following relation:

$\begin{matrix}{V_{redox} = {\frac{RT}{zF}{\ln \left( \frac{\gamma_{H}c_{H}}{\gamma_{L}c_{L}} \right)}}} & (5)\end{matrix}$

where γ_(H) and γ_(L) are the activity coefficients on the highconcentration side (H) and the low concentration side (L) of themembrane, and c_(H) and c_(L) are concentrations of the chloride ion onthe high concentration side (H) and the low concentration side (L) ofthe membrane.

To compare the results obtained with previous experiments, the inventorscalculated molar flux density or permeation rate, p (mol-cm⁻²-h⁻¹),which determined the classical solubility-diffusion model as:

p=PΔC  (6)

Example 7: Calculation of Ionic Conductance and Surface Charge Density

The ionic conductance (G₀) of the membrane was deduced from the slope ofI-V curves, measured in the Ohmic regime at voltages between −10 to +10mV, for equal salt concentrations on both sides of the membrane.

The inventors put forth the simplest model that could predict variationof the membrane's conductivity with the surface charge on the GO flakes,without taking any assumption of the chemistry of GO flakes nor fluidicproperties. The inventors assumed that the surface charge on thenanochannel walls increased the conductivity of nanochannels byincreasing the local concentration of the counterions, to preserve thecharge neutrality within the channel. The total conductivity of thechannel was then given by:

G ₀ =q(μ_(K+)+μ_(Cl−))c _(B) N _(A) wh/l+2μ_(K+)σ_(S) h/l  (7)

where the first part of the equation corresponds to the Ohmicconductance due to the bulk concentration of ions, and the second partis the contribution from the excess counterions; q is the elementarycharge; μ_(K+) and μ_(Cl−) are the ionic mobilities of cations andanions, respectively; N_(A) is Avogadro's number; c_(B) is theelectrolyte's bulk concentration; σ_(S) is the surface charge density; wand l are the width and length of channel, respectively.

Here the left term is the surface-charge governed conductance, whichdominated at low salt concentration, and the right term is the bulkconductance dominant at high concentration. The approximated length ofthe single nanochannel across the membrane was derived from thethickness of the membrane. The width of the single channels wasapproximated to be the lateral sizes of the graphene oxide nanosheets.The G₀ was calculated by dividing the calculated Ohmic conductances bythe number of channels. To obtain the number of channels, the inventorsassumed that measured conductance at high concentration regime i.e.c_(B)=1 M, where the surface charges are mostly screened, was determinedby bulk behaviors.

Example 8: pH-Dependent Ionic Conductances and Surface Charge Densities

FIG. 12B illustrates the surface charge densities of graphene oxidenanochannels, which were calculated using the ionic conductancesobtained at different pH values and molarities (FIG. 12A). The vanishingCOO surface group due to the protonation at low pH led to a reduction inthe surface charge. Dissociation of other groups present on the GOsheets also contributed to the pH-regulated surface charge variation.

Example 9: Effects of Excess Hydronium or Hydroxide Ions

The ionic currents associated with the excess hydronium (H₃O⁺) orhydroxide (OH⁻) ions were subtracted from all drift-diffusion andconductance measurements, since those excess species may significantlycontribute to the ionic conductance as shown in FIG. 13A. In addition,increase of the interlayer spacing was observed at pH 11.7 by around 0.3nm compared to those below pH 10 (FIG. 13B).

Example 10: pH-Dependent Drift-Diffusion Measurements

FIG. 14A is a graph showing current-voltage transport behaviors underasymmetric conditions (10⁻¹ M KCl and varying pH at values of 6.27, 9.18and 11.10 on the feed chamber, and 10⁻² M and constant pH of about 6 onthe permeate chamber).

FIG. 14B is a graph showing current-voltage transport behaviors underasymmetric conditions (10⁻¹ M KCl and varying pH at values of 2.7, 4.0and 5.2 on the feed chamber, and 10⁻² M and constant pH of about 6 onthe permeate chamber).

Example 11: Mean Field Model for Ion Transport in the Nanochannels

When the charged surface is immersed in an electrolyte, theelectrostatic surface potential created by surface charges attractscounter-ions and repels co-ions. The region referred as the diffuseregion of the electrical double layer has a higher density ofcounterions and a lower density of co-ions than the bulk. In thisregime, the electrical potential decays exponentially with distancegiven by Debye length (λ_(D)=κ⁻¹)¹⁰

$\begin{matrix}{\kappa = \left( \frac{q^{2}\Sigma_{i}n_{0}^{(i)}z_{i}^{2}}{ɛ_{0}ɛ_{r}k_{B}T} \right)^{1/2}} & (8)\end{matrix}$

where n₀ ^((i)) is the number density of ions of the type i in the bulk,∈ (=∈₀∈_(r)) is the dielectric constant or permittivity, and k_(B) isthe Boltzmann constant. In a thin region between the surface and thediffuse layer, there is a layer of bound or tightly associatedcounterions, generally defined as the Stern layer.

This region is of the order of one or two solvated ions thick and alsoreferred as the bound part of the double layer. In this region, it wasassumed that the potential falls linearly from the surface to theinterface between the diffuse layer and the Stern layer.

A graphene oxide nanocapillary was modeled as a rectangular channelformed by two separated sheets of graphene oxide separated by thedistance h. The channel was delimited by the pristine graphene on topand bottom, and by oxidized regions of graphene on the sides. The Sternlayer takes into account the finite size of the charged-surfacefunctional groups. An electric field is applied along z-axis. Thefollowing equations were solved along the x-axis. The inventorsconsidered there to be no friction between the water and top/bottomlayers of pristine graphene.

The surface potential (Φ) on the charged walls in the electrolytessatisfies Poisson-Boltzmann equation as below

$\begin{matrix}{{\nabla^{2}\Phi} = {{- \frac{1}{ɛ_{0}ɛ_{r}}}{\sum{zqn}}}} & (9) \\{n = {n_{0}{\exp \left( \frac{{zq}\; \varphi}{k_{B}T} \right)}}} & (10)\end{matrix}$

By combining above two equations,

$\begin{matrix}{{\nabla^{2}\varphi} = {\frac{2{qn}_{0}}{ɛ_{0}ɛ_{r}}{\sinh \left( \frac{q\; \varphi}{k_{B}T} \right)}}} & (11)\end{matrix}$

Stern layer where showing linearly varying potential can be obtained asbelow with regard to boundary conditions

$\begin{matrix}{{\frac{\varphi}{x}(0)} = {{0\mspace{14mu} {and}\mspace{14mu} {\Phi \left( {R - \delta} \right)}} = {{{\Phi_{D} \cdot \Phi_{R}} - \Phi_{D}} = \frac{a\; \delta}{ɛ_{0}{ɛ\delta}}}}} & (12)\end{matrix}$

In order to determine the surface charge density on the walls and thepotential (Φ_(D)), chemical reactions occurred on the oxidized surfaceregime, corresponding to the protonation of carboxyl or hydroxyl groupsas below, were taken into account

GO⁻+H⁺

GOH

GOH+H⁺

GOH₂ ⁺

The equilibrium equations of the above reactions were defined by

$K = {\frac{N_{GO} - \left\lbrack H^{+} \right\rbrack_{0}}{N_{GOH}} = {{10^{- {pK}}\mspace{14mu} {and}\mspace{14mu} L} = {\frac{{N_{GOH}\left\lbrack H^{+} \right\rbrack}_{0}}{N_{{GOH}_{2}^{+}}} = 10^{- {pL}}}}}$

where the hydrogen activity at the surfaces is

$\left\lbrack H^{+} \right\rbrack_{0} = {\left\lbrack H^{+} \right\rbrack_{bulk}{\exp \left( \frac{q\; \varphi_{s}}{k_{B}T} \right)}}$

and N_(i) is the density of surface sites.

By taking into account the total surface density of active sites andsurface charge density, the Behriens-Grier equation could be obtained

$\begin{matrix}{{{10^{{pL} - {p\; H}}\left( {\sigma - {q\; \Gamma}} \right){\exp \left( {{- 2}\frac{q\; \varphi_{R}}{k_{B}T}} \right)}} + {\sigma \; {\exp \left( {- \frac{q\; \varphi_{R}}{k_{B}T}} \right)}} + {10^{{p\; H} - {pK}}\left( {\sigma - {q\; \Gamma}} \right)}} = 0} & (13)\end{matrix}$

where the total surface density of activity sites (Γ) is ΣN_(i)=ΣN_(GOH)₂ ₊ +N_(GOH) ⁻ +N_(GOH). Here, pK and pL do not correspond to bulkvalues for protonation of carboxyl and hydroxyl groups, they areeffective equilibrium constants chosen as to match the experimentalresults.

And the Grahame equation was applied to calculate the surface chargedensity associated with the double layer potential

$\begin{matrix}{{\sigma \left( \Phi_{D} \right)} = {\frac{2k_{B}T\; ɛ_{0}ɛ_{r}}{q\; \lambda_{D}}{\sinh \left( \frac{q\; \varphi_{D}}{2k_{B}T} \right)}}} & (14)\end{matrix}$

By solving equations (12) and (13) self-consistently with regard to

${{\Phi_{R} - \Phi_{D}} = \frac{\sigma\delta}{ɛ_{0}ɛ_{r}}},$

it gives the surface charge density and the surface density of eachspecies N_(i) as a function of pH, electrolyte concentration, and thefour chemical parameters, Γ, δ, pK and pL.

In order to model the conductances across the membranes, the iondistribution and velocity field in the nanochannels was calculated withthe Navier-Stokes equation and Boltzmann distribution, assuming thatinertial and pressure terms are negligible and a no-slip condition atx=R.

$\begin{matrix}{{n_{+}(x)} = {{n_{o}{\exp \left( {- \frac{q\; {\varphi (x)}}{k_{B}T}} \right)}\mspace{14mu} {and}\mspace{14mu} {n_{-}(x)}} = {n_{0}{\exp \left( \frac{q\; {\varphi (x)}}{k_{B}T} \right)}}}} & (15) \\{{\rho\left( {\frac{\partial\overset{->}{u}}{\partial t} + {\overset{->}{u} \cdot \overset{}{\nabla u}}} \right)} = {{- {\overset{->}{\nabla}P}} + {\eta {\nabla^{2}\overset{->}{u}}} + {n\overset{->}{E}}}} & (16)\end{matrix}$

wherein inertial and pressure terms are negligible compared to viscosityand electrostatic force, and n{right arrow over(E)}=−∈₀∈_(r)E_(z)∇²Φ(x){right arrow over (z)} is given. Therefore,

∇²′(ηu(x)−∈₀∈_(r) E _(z)Φ(x))=0  (17)

with regard to the boundary conditions (no-slip boundary condition),

${\frac{u}{x}(0)} = {{0\mspace{14mu} {and}\mspace{14mu} {u(R)}} = 0.}$

The inventors obtained the solution as

$\begin{matrix}{{u(x)} = {\frac{ɛ_{0}ɛ_{r}E_{z}}{\eta}\left( {{\Phi (x)} - \Phi_{0}} \right)}} & (18)\end{matrix}$

The current was produced by the drifting of ions under the electricfield and by the flow of water carrying the ions

I _(±) ^(drift)=2hqμ _(±) E _(z)∫₀ ^(R) n _(±)(x)dx  (19)

I _(±) ^(diffusion)=±2hq∫ ₀ ^(R) n _(±)(x)u(x)dx  (20)

Finally, the inventors were able to obtain the conductance as

$G = {{\frac{I_{total}}{V_{z}}\mspace{14mu} {with}\mspace{14mu} V_{z}} = {E_{z} \times {L_{channel}.}}}$

Example 12: Validation of the Analytical Continuum Models

In order to validate the model as shown in FIG. 15, the analysis wasalso carried out with a rectangular channel possessing charge polarityon planar surfaces and a cylindrical pore, respectively.

FIG. 16 is a figure demonstrating the nanochannel with charge-polarizedplanar sheets. The highly concentrated counterions between two polarizednanosheets resulted in overestimated ionic conductance under electricfield gradients compared to experimental values at different pH andmolarities. Deviation in the ionic conductance indicates that dominantconducting pathways of ions in the graphene oxide membranes shouldconsist of two dimensional, pristine graphene nanocapillaries withpartially charged regions, not fully functionalized channels. Theinvestigation was also carried out for a quasi-one dimensionalcylindrical nanochannel with surface charges on circumference ofcylindrical channel (FIG. 17). These models were inconsistent withexperimental observations.

Example 13: Ion Strength-Dependent Ionic Conductance and CationPermselectivity

FIG. 18A is a graph showing current-voltage curves measured at differentsalt concentrations at around pH 5.5. Inset shows the rectificationfactor RF as a function of molarity, describing the relative ratio ofthe measured currents at scan voltages of ±80 mV.

FIG. 18B is a graph showing current-voltage curves obtained fromdifferent feed concentrations and the constant concentration gradient ofC_(High)/C_(Low)=10 at pH 5.5. Inset shows the increasing membranepotentials with dilution of the electrolytes (feed molarity c_(F)),associated with the enhancement of the cation selectivity.

While the present invention has been particularly shown and describedwith reference to exemplary embodiments thereof, it will be understoodby those of ordinary skill in the art that various changes in form anddetails may be made therein without departing from the spirit and scopeof the present invention as defined by the following claims.

What is claimed is:
 1. A method of preparing a graphene-based membrane,the method comprising a) providing a stacked arrangement of layers of agraphene-based material, wherein the layers of the graphene-basedmaterial define one or more nanochannels between neighboring layers, andb) varying an electrical charge on a surface of the layers of thegraphene-based material defining the one or more nanochannels to controlsize selectivity and/or ionic selectivity of the graphene-basedmembrane.
 2. The method according to claim 1, wherein providing thestacked arrangement of layers of a graphene-based material comprises a)providing a suspension comprising layers of the graphene-based materialdispersed therein, b) filtering the suspension through a poroussubstrate to dispose the layers of the graphene-based material as astacked arrangement on the porous substrate, and c) separating thestacked arrangement of layers of the graphene-based material from theporous substrate.
 3. The method according to claim 2, wherein providingthe suspension comprising layers of a graphene-based material dispersedtherein comprises a) sonicating a dispersion comprising thegraphene-based material to exfoliate the graphene-based material intolayers, and b) removing graphene-based material which are present asmultilayer crystals from the dispersion to obtain the suspension.
 4. Themethod according to claim 2, further comprising arranging the stackedarrangement of layers of the graphene-based material on a supportingsubstrate.
 5. The method according to claim 4, wherein the supportingsubstrate is a further membrane comprising an array of nanopores.
 6. Themethod according to claim 1, wherein varying an electrical charge on asurface of the layers of the graphene-based material defining the one ormore nanochannels comprises at least one of (i) varying polarity of theelectrical charge; (ii) varying magnitude of the electrical charge, or(iii) arranging layers of opposite electrical charges in the stackedarrangement.
 7. The method according to claim 1, wherein varying anelectrical charge on a surface of the layers of the graphene-basedmaterial defining the one or more nanochannels comprises carrying out atleast one of (i) a chemical substitution process on the graphene-basedmaterial, (ii) a reduction process on the graphene-based material, or(iii) contacting the graphene-based material with a liquid reagent andvarying molarity and/or pH of the liquid reagent.
 8. The methodaccording to claim 1, further comprising applying pressure to a surfaceof the stacked arrangement of layers of the graphene-based material. 9.A graphene-based membrane comprising a stacked arrangement of layers ofa graphene-based material, the layers of the graphene-based materialdefining one or more nanochannels between neighboring layers, wherein asurface of the layers of the graphene-based material defining the one ormore nanochannels possess an electrical charge, and wherein the layersof the graphene-based material are configured to control sizeselectivity and/or ionic selectivity of the graphene-based membrane byvarying the electrical charge.
 10. The graphene-based membrane accordingto claim 9, wherein the graphene-based material comprises grapheneoxide.
 11. The graphene-based membrane according to claim 9, wherein theneighboring layers of the graphene-based material are spaced apart by adistance in the range of about 0.5 nm to about 2 nm.
 12. Thegraphene-based membrane according to claim 9, wherein the layers of thegraphene-based material has a lateral dimension in the range of about0.1 μm to about 10 μm.
 13. The graphene-based membrane according toclaim 9, wherein the stacked arrangement of layers of a graphene-basedmaterial is arranged on a supporting substrate.
 14. The graphene-basedmembrane according to claim 13, wherein the supporting substrate is afurther membrane comprising an array of nanopores, and wherein thefurther membrane is formed of a material selected from the groupconsisting of SiN_(x), carbon foam, ceramic membrane, and polymericmembrane.
 15. The graphene-based membrane according to claim 9, whereinthe layers of the graphene-based material are configured to control sizeand/or ionic selectivity of the graphene-based membrane by varying atleast one of (i) polarity of the electrical charge; (ii) magnitude ofthe electrical charge, or (iii) arranging layers of opposite electricalcharges in the stacked arrangement.
 16. The graphene-based membraneaccording to claim 9, wherein the graphene-based membrane is configuredto reject ions having a radius of hydration of at least about 4.5 Å. 17.A method of separating ions from a fluid stream, the method comprisinga) providing a graphene-based membrane comprising a stacked arrangementof layers of a graphene-based material, the layers of the graphene-basedmaterial defining one or more nanochannels between neighboring layers,wherein a surface of the layers of the graphene-based material definingthe one or more nanochannels possess an electrical charge, and whereinthe layers of the graphene-based material are configured to control sizeselectivity and/or ionic selectivity of the graphene-based membrane byvarying the electrical charge, and b) directing a fluid streamcomprising one or more ions towards a first surface of thegraphene-based membrane, wherein ions to be separated from the fluidstream are filtered through the graphene-based membrane.
 18. The methodaccording to claim 17, wherein directing the fluid stream comprising oneor more ions towards a first surface of the graphene-based membrane iscarried out without an electrical field.
 19. The method according toclaim 17, wherein directing the fluid stream comprising one or more ionstowards a first surface of the graphene-based membrane is carried outwith an electrical field.
 20. The method according to claim 19, whereinthe method of separating ions from a fluid stream is applied toelectrodialysis.